Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include<cstdio>
#include<algorithm>
using namespace std;
int main(void)
{
	int a1,b,c,d,i,j,a[1000],n,flg[1000],p1,p2;
	double mx,xx;
	scanf("%d",&n);
	for(i=0;i<n;i++)	scanf("%d",&a[i]);
	for(i=0;i<n;i++)	flg[i]=0;
	sort(a,a+n);
	mx=-1.0;
	for(i=0;i<n-1;i++)	{
		c=a[i];
		flg[i]=1;
		for(j=i+1;j<n;j++)	{
			d=a[j];
			flg[j]=1;
			p1=n-1;
			while(1)	{
				if(flg[p1]==0)	{
					a1=a[p1];
					flg[p1]=1;
					break;
				}
				p1--;
			}
			p2=n-1;
			while(1)	{
				if(flg[p2]==0)	{
					b=a[p2];
					flg[p2]=1;
					break;
				}
				p2--;
			}
//			printf("a=%d b=%d c=%d d=%d\n",a1,b,c,d);	
			xx=(double)(a1+b)/(d-c);
			mx=max(xx,mx);
//			printf("%lf\n",xx);
			flg[j]=0;	flg[p1]=0;	flg[p2]=0;			
//			printf("i=%d j=%d\n",i,j);
		}
		flg[i]=0;
	}
	printf("%lf\n",mx);
	
    return 0;
}